Data-driven wind farm frequency control method based on dynamic mode decomposition

ABSTRACT

A data-driven wind farm frequency control method based on dynamic mode decomposition. The method enables a low-dimension nonlinear dynamic feature of a wind power system to perform global capturing in a high-dimension space through a state transition matrix given by a Koopman operator theory, thus fewer data samples are necessary while control requirements are satisfied with respect to a model fitting accuracy. Meanwhile, a pure linear feature of a control model also provides a favorable foundation for fast on-line dynamic response, thereby satisfying response accuracy and speed requirements simultaneously in an actual control step.

FIELD OF TECHNOLOGY

The present invention belongs to the technical field of power and inparticular, relates to a data-driven wind farm frequency control methodbased on dynamic mode decomposition.

BACKGROUND

Due to increasingly prominent environmental problems and energy crisiscaused by fast consumption of conventional fossil energy, conventionalenergy demand of a power system is being gradually replaced byenvironment-friendly, efficient and sustainable clean energy, of whichwind power has become an investment and construction focus worldwide asthe most promising clean energy. With Europe as an example, installedcapacity of wind power in Europe has increased at a rate of about 10 GWeach year continuously in the recent 10 years. As of 2019, installedcapacity of wind power in Europe reached 205 GW and wind power outputreached as high as 15%, wherein domestic wind power output of Denmarkreached as high as 48%. High wind power penetration rate brings a newchallenge for operation control of a current grid and frequencystability of the grid is an important step thereof. With access of alarge number of speed-variable wind turbines to the grid through powerelectronic converters, an active output and a frequency of a wind sitepresent decoupling features of power electronic, resulting in reductionof overall equivalent inertia of a system and more serious frequencyfluctuation of the grid under a same load disturbance, which are dangersfor safe and stable operation of the grid. Therefore, the grid operationcode of the world gradually uses capacity of the wind power forparticipation in frequency modulation as the precondition for gridentry. For example, Hydro-Quebec grid code of Canada requires that awind farm having an installed capacity above 10 MW should be equippedwith frequency correction control capacity. For China, the new Guide onSecurity and Stability for Power System prescribes that a wind powerstation and a photovoltaic power station of 35 kV and above should beequipped with a primary frequency modulation capability.

The technical solution for the current wind power to participate in theprimary frequency modulation of the grid can be divided into amodel-driven type and a data-driven type. With a model-driven controlpolicy, a wind turbine dynamic model is built based on cognitive priorsabout a wind turbine energy transformation model. However, since a largenumber of device parameters in the site need to be measured andmaintained regularly one by one, thus it is difficult to ensure accuracyand effectiveness of the model. As for a data-driven method, segmentallinear fitting plays a major role currently. Methods of such type canbuild a dynamic model of a wind turbine through historical data.However, the segmental linear thinking pattern can not solve thenonlinear problem still of the wind turbine dynamic feature in differentwork conditions, as generally it is difficult for segmental number tobalance conciseness and accuracy of the model. Therefore, it isnecessary to study a wind turbine dynamic modeling and control method bycombining model-driven and data-driven advantages, so as to adapt toactual requirements for fast and flexible participation of a wind sitein grid frequency dynamic response.

SUMMARY

For the above problems, the present invention provides a data-drivenwind farm frequency optimization control method based on dynamic modedecomposition. The optimization control method mainly consists of twomodules: a wind turbine dynamic mode decomposition module and a windfarm frequency optimization control module. The specific steps ofimplementing optimization control comprises: measuring a wind turbinestate in a wind farm at time t and transmitting it to a controller;performing wind turbine dynamic mode decomposition in the controller andcalculation of an active frequency control instruction; and obtaining acontrol command at time t+1, thus transmitting it to the wind farm.

An object of the present invention for applying the optimization controlmethod is a wind turbine generator system in a large wind site. Sincethe current investment and construction of a double-feed asynchronouswind turbine are of the largest scale, in an exemplary way, a controlobject is set as a double-feed asynchronous wind turbine. Meanwhile,wind turbines having similar operation situations and device parametersin the site can be aggregated into one unit for control.

For convenient statement, setting a local control step of thedouble-feed asynchronous wind turbine can enable an active output of anconverter to be adjusted with an external active instruction. Meanwhile,rotation speed is locally controlled through a propeller pitch angle forconstraint protection.

The data-driven wind farm frequency optimization control method based ondynamic mode decomposition specifically comprises the following steps:

S1: Building an Initial Data Set

building a state equation of a power generation unit from a frequencymodulation control perspective, as indicated by formula (1)

ω_(k+1) =f(ω_(k) ,u _(k))  (1)

wherein ω_(k) denotes a wind turbine rotation speed at time k, f denotesa nonlinear state transition relation function and an input variableu_(k) is defined as:

$\begin{matrix}{u_{k} = \begin{bmatrix}P_{{ref},k} \\v_{w,k}\end{bmatrix}} & (2)\end{matrix}$

wherein, P_(ref,k) is an active instruction of an external input andv_(w,k) is a current wind speed. From a data driving perspective, adynamic feature thereof should be restored according to historical dataaccumulated in a wind turbine operation process. However, such statetransition relation is mainly comprised in a data pair having a timingsequence correspondence relation, which is denoted as:

X=[x ₁ x ₂ . . . x _(N)],Y=[y ₁ y ₂ . . . y _(N)]  (3)

wherein,

$\left( {{x_{k} = \ \begin{bmatrix}\omega_{k} \\u_{k}\end{bmatrix}},{y_{k} = \ \begin{bmatrix}\omega_{k + 1} \\u_{k + 1}\end{bmatrix}}} \right)$

is a data pair at time k, with N pairs in total, and wherein, ω_(k+1)and u_(k+1) respectively denote a state quantity and an input quantityof a next step size. It should be noted that data matrices can becolumn-exchanged, as long as two matrices therebetween satisfy thecolumn correspondence relation.

S2: Dynamic Mode Decomposition

A mode can be understood as an inherent element in a wind turbinedynamic feature. For a double-feed asynchronous wind turbine, aninitiative nonlinear dynamic feature thereof comes from a wind energytransformation process described in a wind energy transformationequation.

p _(m)=½ρA _(rot) c _(p)(λ,θ)v _(w) ³  (4)

Wherein, p_(m) is a mechanical power captured by a wind turbine blade; ρis an air density; A_(rot) is an area of a wind-affected section decidedby a radius of a wind turbine blade; and c_(p) is a wind energyutilization rate of a wind turbine as a nonlinear function of a windturbine tip speed ratio

$\lambda = \frac{\omega R}{\upsilon_{\omega}}$

and a blade propeller pitch angle θ, wherein, ω is a wind turbinerotation speed, R is a radius of a wind turbine blade and v_(w) is acurrent wind speed. It can be seen from formula (4) that the wind energytransformation model enables presence of a strong nonlinear couplingrelation between the state quantity and the input quantity of the windturbine, which is a great challenge for solution of the optimizationcontrol problem. If a model-driven modeling policy is adopted,estimation or measurement of multiple parameters are certainly involvedtherein, resulting in the difficulty for ensuring control effects in ascene where the model is not complete. A dynamic mode decompositionthinking pattern involves mapping a low-dimension nonlinear dynamicprocess to a high-dimension observation space through an observationfunction based on cognitive priors about a wind turbine physical model,enabling a nonlinear dynamic feature of a low-dimension space to presenta linear trend in a high-dimension space, such that a dynamic featurethereof is decomposed with a matrix linear algebra operation. Thethinking pattern can not only perform a data-driven flexibilityadvantage, without abandoning a model-driven theoretical foundation, butalso enable acquisition of an accurate dynamic mode with fewer samples.

Specifically, for state data (ω_(k),u^(k)) at time k, an observationfunction Ψ effects, thereby obtaining a high-dimension observation statevector:

$\begin{matrix}{{\Psi\left( {\omega_{k},u_{k}} \right)} = {\begin{bmatrix}\omega_{k} \\\frac{1}{\upsilon_{\omega,k}} \\e^{{- {0.1}}\omega_{k}\upsilon_{\omega,k}} \\\omega_{k}^{2} \\u_{k}\end{bmatrix} = \begin{bmatrix}{\psi\left( {\omega_{k},u_{k}} \right)} \\u_{k}\end{bmatrix}}} & (5)\end{matrix}$

It can be seen that a mapping-transformed vector and an initial statevector are maintained at a same dimensional number level. Thus, theoperation does not add a burden of processing too much data. A mappingtransformation effects for each column of an initial data set, therebyobtaining a high-dimension observation set matrix:

X _(lift)=[Ψ(ω₁ ,u ₁)Ψ(ω₂ ,u ₂) . . . Ψ(ω_(N) ,u _(N))]

Y _(lift)=[Ψ(ω₂ ,u ₂)Ψ(ω₃ ,u ₃) . . . Ψ(ω_(N+1) ,u _(N+1))]  (6)

For trail data of a high-dimension observation space, a high-dimensionlinear dynamic feature of a wind turbine can be fitted through a statetransition matrix value of limited dimensions according to relatedtheories of a Koopman operator, that is, a search matrix A enables∥Y_(lift)−A_(lift)X_(lift)∥₂ to be minimum; and an optimization problemis solved and a wind turbine dynamic model is obtained through analgebra operation as follows:

A _(lift) =Y _(lift) X _(lift) ^(†)  (7)

Wherein, † denotes a pseudo-inverse operation of a matrix. From acontrol perspective, it is also necessary to split a matrix A_(lift)according to dimensional number of a high-dimension observation spaceand dimensional number of an input quantity; for a high-dimensionmapping function structure employed by the method, a sub-block on a leftupper side 4×4 of a matrix A_(lift) is split as a state transitionmatrix A of a dynamic equation, and a sub-block on a right upper side4×2 of a matrix A_(lift) is split to obtain an input matrix B. By now, awind turbine high-dimension linear dynamic model via dynamic modedecomposition can be represented as the following form:

ψ(θ_(k+1) ,u _(k+1))=Aψ(ω_(k) ,u _(k))+Bu _(k)  (8)

S3: A Central Wind Site Control Model

According to a dynamic mode decomposition method, a dynamic model of Mpower generation units in a wind site can be obtained.

ψ(ω_(k+1) ^(i) ,u _(k+1) ^(i))=A _(i)ψ(ω_(k) ^(i) ,u _(k) ^(i))+B _(i) u_(k) ^(i)=1,2, . . . ,M  (9)

on such a basis, a state vector in a central control model is defined asfollows:

$\begin{matrix}{\chi_{k} = \begin{bmatrix}{\psi\left( \omega_{k}^{1},u_{k}^{1} \right)} \\\vdots \\{\psi\left( {\omega_{k}^{M},u_{k}^{M}} \right)}\end{bmatrix}_{4M \times 1}} & (10)\end{matrix}$

meanwhile, an input vector in a central control model is defined asfollows:

$\begin{matrix}{\eta_{k} = \begin{bmatrix}u_{k}^{1} \\\vdots \\u_{k}^{M}\end{bmatrix}_{2M \times 1}} & (11)\end{matrix}$

A control model corresponding to a central state vector is provided fromformula (9):

χ_(k+1) =Aχ _(k) +Bη _(k)  (12)

Wherein, a matrix A,B can be structured according to the followingdiagonal forms by a state transition matrix of each power generationunit:

$\begin{matrix}{A = \begin{bmatrix}A_{1} & \; & \; \\\; & \ddots & \; \\\; & \; & A_{M}\end{bmatrix}} & (13) \\{B = \begin{bmatrix}B_{1} & \; & \; \\\; & \ddots & \; \\\; & \; & B_{M}\end{bmatrix}} & (14)\end{matrix}$

Wherein, A₁ . . . A_(M) respectively denotes a state transition matrixof M power generation units, and B₁ . . . B_(M) respectively denotes aninput matrix of M power generation units.

It can be seen that the matrix A,B structured in this manner is providedwith a special sparsity structure, so as to provide more convenientconditions for fast solution of an on-line dynamic optimization controlproblem.

S4: On-Line Dynamic Optimization

On the basis of obtaining a wind turbine linear dynamic model through adata-driven method, a wind site dynamic optimization control algorithmcan be represented as indicated by formula (15) according to a generalform of a model prediction and control framework:

$\begin{matrix}{{\min\limits_{u_{k},\chi_{k}}{{J\left( {\left( \upsilon_{k} \right)_{k = 0}^{T - 1},\left( \chi_{k} \right)_{k = 0}^{T}} \right)}\mspace{14mu}{subject}\mspace{14mu}{to}}}{{\chi_{k + 1} = {{A\chi_{k}} + {B\;\upsilon_{k}}}},{k = 0},\ldots\mspace{14mu},{T - 1}}{{{{E_{k}\chi_{k}} + {F_{k}\upsilon_{k}}} \leq b_{i}},{k = 0},\ldots\mspace{14mu},{T - 1}}{{E_{T}\chi_{T}} \leq b_{T}}} & (15)\end{matrix}$

Wherein, T is a prediction range length of a model prediction andcontrol algorithm and a target function J is shown in the followingform:

$\begin{matrix}{{J\left( {\left( \upsilon_{k} \right)_{k = 0}^{T - 1},\left( \chi_{k} \right)_{k = 0}^{T}} \right)} = {{\chi_{T}^{T}Q_{T}\chi_{T}} + {q_{T}^{T}\chi_{T}} + {\sum\limits_{k = 0}^{T - 1}{\chi_{k}^{T}Q_{k}\chi_{k}}} + {\upsilon_{k}^{T}R_{k}\upsilon_{k}} + {q_{k}^{T}\chi_{k}} + {r_{k}^{T}\upsilon_{k}}}} & (16)\end{matrix}$

Wherein, Q_(k), Q_(T) is a positive semi-definite target coefficientmatrix of a state variable at time k and time T, R_(k) is a positivesemi-definite target coefficient matrix of an input variable at time k,q_(k) ^(τ), q_(T) ^(τ) is a target coefficient vector of a statevariable at time k and time T, r_(k) ^(τ) is a target coefficient vectorof an input variable at time k, E_(k) is a state variable boundaryconstraint coefficient matrix at time k, F_(k) is an input variableboundary constraint coefficient matrix at time k, and b_(k) is aboundary constraint coefficient vector at time k. Design of acoefficient matrix and a coefficient vector depends on a wind sitedynamic optimization control objective. Q_(k), R_(k) is a positivesemi-definite coefficient matrix, a matrix E_(k), F_(k) and a vectorb_(k) correspond to a state quantity at time k and a boundary constraintof an input quantity respectively, E_(T), b_(T) is a boundary constraintof a state quantity at time T, and χ_(T) is a state quantity at time T.Design of a coefficient matrix and a coefficient vector depends on awind site dynamic optimization control objective.

In the problem of frequency modulation for wind power, the controlobjective needs to be optimized in two aspects: wind farm activefrequency modulation instruction's following effect and transientstability of a rotation speed of a power generation unit. Therefore, byusing a fluctuation degree of a wind turbine rotation speed to measureits transient stability, the following optimization objective is given:

$\begin{matrix}{\min\limits_{P_{ref}}{\sum\limits_{i = 1}^{M}\left( {{\sum\limits_{k = 0}^{T - 1}{{{\Delta P_{{ref},k}^{i}} - {K_{df}\Delta\; f}}}_{2}} + {Q_{x}{\sum\limits_{k = 0}^{T - 1}{{\omega_{k + 1}^{i} - \omega_{k}^{i}}}_{2}}}} \right)}} & (17)\end{matrix}$

Wherein, an active adjusting amount ΔP_(ref,k) ^(i) is defined as:

ΔP _(ref,k) ^(i) =P _(ref,k) ^(i) −P _(MPPT,k) ^(i)  (18)

formula (18) denotes an adjusting amount of a wind turbine activeinstruction P_(ref,k) ^(i) relative to a control instruction P_(MPPT,k)^(i) provided by a local controller under a maximum power trackingmodel.

ΔP _(ref,k) ^(i) =P _(ref,k) ^(i) −P _(deload,k) ^(i) =P _(ref,k) ^(i)−R _(d) ·P _(MPPT,k) ^(i)  (19)

wherein, P_(deload,k) ^(i) is an active instruction of a load-reductionwork mode and R_(d) is a load-reduction amplitude coefficient; afrequency offset amount is defined as:

Δf=f _(meas) −f _(ref)  (20)

formula (20) denotes an offset amount of a grid entry point measurementfrequency f_(meas) relative to a reference frequency f_(ref). Aparameter K_(df) is a droop coefficient of a wind farm in an externalpower-frequency feature curve and Q_(x) is a weighting coefficient forbalancing two optimization objectives. By adjusting an activeinstruction based on a local control instruction, a first item

$\sum\limits_{i = 1}^{M}{\sum\limits_{k = 0}^{T - 1}{{{\Delta P_{{ref},k}^{i}} - {K_{df}\Delta\; f}}}_{2}}$

of an optimization objective in formula (17) enables allocation of awind turbine frequency modulation task to be performed on the basis ofconsidering a respective power generation level so as to enable anoverall allocation of an active output to correspond to a wind turbinelocal working condition, such that a wind farm group also ensuresoverall wind energy transformation effects of the wind farm group whileproviding a frequency modulation service. By optimizing a fluctuationdegree of a wind turbine rotation speed, a second item

$Q_{x}{\sum\limits_{i = 1}^{M}{\sum\limits_{k = 0}^{T - 1}{{\omega_{k + 1}^{i} - \omega_{k}^{i}}}_{2}}}$

of an optimization objective enables a wind turbine operation state morestable, so as to reduce mechanical fatigue of a wind turbine which iscaused by participation of the wind turbine in a frequency modulationresponse process, and is added to a gearbox and other fragile mechanicalcomponents, thereby prolonging the service life of the wind turbine.

On the basis of the optimization objective, a timing sequenceconstraint, a state quantity boundary constraint, an input constraintand an initial state constraint of a central state vector are providedand respectively indicated as formula (21), formula (22), formula (23)and formula (24):

χ_(k+1) =Aχ _(k) +Bv _(k) ,k=0,1, . . . ,T−1  (21)

ω_(min)

ω_(k) ^(i)=ψ(ω_(k) ^(i) ,u _(k) ^(i))(1)

ω_(max) ,i=1, . . . ,M,k=1, . . . ,T  (22)

P _(ref,min)

u _(k) ^(i)(1)

P _(ref,max) ,k=0,1, . . . ,T−1  (23)

χ₀=[ψ(ω₀ ¹ ,u ₀ ¹) . . . ψ(ω₀ ^(M) ,u ₀ ^(M))]^(τ)  (24)

Wherein, χ₀ denotes an initial state of a central state vector χ_(k),and

formula (17) to formula (24) constitute a complete wind farm frequencydynamic optimization control method. Since both a constraint conditionand a target function have concavity, thus the entire model constitutesa secondary planning problem belonging to convex optimization, which canbe rapidly and accurately solved through the current optimizationsolution procedure.

The present invention provides a data-driven control method based ondynamic mode decomposition for dynamic frequency control of a high-ratewind power independent power system. The method enables a low-dimensionnonlinear dynamic feature of a wind power system to perform globalcapturing in a high-dimension space through a state transition matrixprovided by a Koopman operator theory, thus fewer data samples arenecessary while control requirements are satisfied with respect to amodel fitting accuracy. Meanwhile, a pure linear feature of a controlmodel also provides a favorable foundation for fast on-line dynamicresponse, thereby satisfying response accuracy and speed requirementssimultaneously in an actual control step.

Other features and advantages of the present invention will be stated inthe subsequent description and partially become apparent from thedescription or will be understood by implementing the present invention.The purpose and other advantages of the present invention can berealized and obtained by a structure as pointed out in the description,claims and accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

To describe the technical solutions in the embodiments of the presentinvention or in the prior art more clearly, the following brieflydescribes the accompanying drawings required for describing theembodiments or the prior art. Apparently, the accompanying drawings inthe following description show some embodiments of the presentinvention, and the person skilled in the art may still derive otherdrawings from these accompanying drawings without creative efforts.

FIG. 1 shows a wind farm frequency optimization control module relationbased on dynamic mode decomposition according to embodiments of thepresent invention; and

FIG. 2 shows implementation steps of wind farm frequency optimizationcontrol based on dynamic mode decomposition according to embodiments ofthe present invention.

DESCRIPTION OF THE EMBODIMENTS

To make the objectives, technical solutions, and advantages of theembodiments of the present invention clearer, the following clearly andcompletely describes the technical solutions in the embodiments of thepresent invention with reference to the accompanying drawings in theembodiments of the present invention. Apparently, the describedembodiments are some but not all of the embodiments of the presentinvention. All other embodiments obtained by the person skilled in theart based on the embodiments of the present invention without creativeefforts fall within the protection scope of the present invention.

The present invention provides a data-driven wind site frequencyoptimization control method based on dynamic mode decomposition. FIG. 1shows a wind farm frequency optimization control module relation basedon dynamic mode decomposition. It can be known from FIG. 1 that theoptimization control method mainly consists of two modules: a windturbine dynamic mode decomposition module and a wind farm frequencyoptimization control module. FIG. 2 shows implementation steps of windfarm frequency optimization control based on dynamic mode decomposition.It can be known from FIG. 2 that the implementation steps ofoptimization control comprises: measuring a wind turbine state in a windfarm at time t and transmitting it to a controller; performing windturbine dynamic mode decomposition in the controller and calculation ofan active frequency control instruction; and obtaining a control commandat time t+1, thus transmitting it to the wind farm.

An object of the present invention for applying the optimization controlmethod is a wind turbine generator system in a large wind site. Sincethe current investment and construction of a double-feed asynchronouswind turbine are of the largest scale, in an exemplary way, a controlobject is set as a double-feed asynchronous wind turbine. Meanwhile,wind turbines having similar operation situations and device parametersin the site can be aggregated into one unit for control.

For convenient statement, setting a local control step of thedouble-feed asynchronous wind turbine can enable an active output of aninverter to be adjusted with an external active instruction. Meanwhile,rotation speed is locally controlled through a propeller pitch angle forconstraint protection.

The data-driven wind farm frequency optimization control method based ondynamic mode decomposition specifically comprises the following steps:

S1: Building an Initial Data Set

building a state equation of a power generation unit from a frequencymodulation control perspective, as indicated by formula (1)

ω_(k+1) =f(ω_(k) ,u _(k))  (1)

wherein, ω_(k) denotes a wind turbine rotation speed at time k, fdenotes a nonlinear state transition relation function and an inputvariable u_(k) is defined as:

$\begin{matrix}{u_{k} = \begin{bmatrix}P_{{ref},k} \\\upsilon_{\omega,k}\end{bmatrix}} & (2)\end{matrix}$

wherein, P_(ref,k) is an active instruction of an external input andv_(w,k) is a current wind speed; From a data driving perspective, adynamic feature thereof should be restored according to historical dataaccumulated in a wind turbine operation process. However, such statetransition relation is mainly comprised in a data pair having a timingsequence correspondence relation, which is denoted as:

X=[x ₁ x ₂ . . . x _(N)],Y=[y ₁ y ₂ . . . y _(N)]  (3)

wherein,

$\left( {{x_{k} = \ \begin{bmatrix}\omega_{k} \\u_{k}\end{bmatrix}},{y_{k} = \ \begin{bmatrix}\omega_{k + 1} \\u_{k + l}\end{bmatrix}}} \right)$

is a data pair at time k, with N pairs in total, and wherein ω_(k+1) andu_(k+1) respectively denote a state quantity and an input quantity of anext step size. It should be noted that a data matrix can becolumn-exchanged, as long as two matrices therebetween satisfy thecolumn correspondence relation.

S2: Dynamic Mode Decomposition

A mode can be understood as an inherent element in a wind turbinedynamic feature. For a double-feed asynchronous wind turbine, aninitiative nonlinear dynamic feature thereof comes from a wind energytransformation process described in a wind energy transformationequation.

p _(m)=½ρA _(rot) c _(p)(λ,θ)v _(w) ³  (4)

Wherein, p_(m) is a mechanical power captured by a wind turbine blade; ρis an air density; A_(rot) is an area of a wind-affected section decidedby a radius of a wind turbine blade; and c_(p) is a wind energyutilization rate of a wind turbine as a nonlinear function of a windturbine tip speed ratio

$\lambda = \frac{\omega R}{\upsilon_{\omega}}$

and a blade propeller pitch angle θ, wherein ω is a wind turbinerotation speed, R is a radius of a wind turbine blade and v_(w) is acurrent wind speed. It can be seen from formula (4) that the wind energytransformation model enables presence of a strong nonlinear couplingrelation between the state quantity and the input quantity of the windturbine, which is a great challenge for solution of the optimizationcontrol problem. If a model-driven modeling policy is adopted,estimation or measurement of multiple parameters are certainly involvedtherein, resulting in difficulty for ensuring control effects in a scenewhere the model is not complete. A dynamic mode decomposition thinkingpattern involves mapping a low-dimension nonlinear dynamic process to ahigh-dimension observation space through an observation function basedon cognitive priors about a wind turbine physical model, enabling anonlinear dynamic feature of a low-dimension space to present a lineartrend in a high-dimension space, such that a dynamic feature thereof isdecomposed with a matrix linear algebra operation. The thinking patterncan not only perform a data-driven flexibility advantage, withoutabandoning a model-driven theoretical foundation, but also enableacquisition of an accurate dynamic mode with fewer samples.

Specifically, for state data (ω_(k), u_(k)) at time k, an observationfunction Ψ effects, thereby obtaining a high-dimension observation statevector:

$\begin{matrix}{{\Psi\left( {\omega_{k},u_{k}} \right)} = {\begin{bmatrix}\omega_{k} \\\frac{1}{\upsilon_{\omega,k}} \\e^{{- {0.1}}\omega_{k}\upsilon_{\omega,k}} \\\omega_{k}^{2} \\u_{k}\end{bmatrix} = \begin{bmatrix}{\psi\left( {\omega_{k},u_{k}} \right)} \\u_{k}\end{bmatrix}}} & (5)\end{matrix}$

It can be seen that a mapping-transformed vector and an initial statevector are maintained at a same dimensional number level. Thus, theoperation does not add a burden of processing too much data. A mappingtransformation effects for each column of an initial data set, therebyobtaining a high-dimension observation set matrix:

X _(lift)=[Ψ(ω₁ ,u ₁)Ψ(ω₂ ,u ₂) . . . Ψ(ω_(N) ,u _(N))]

Y _(lift)=[Ψ(ω₂ ,u ₂)Ψ(ω₃ ,u ₃) . . . Ψ(ω_(N+1) ,u _(N+1))]  (6)

For trail data of a high-dimension observation space, a high-dimensionlinear dynamic feature of a wind turbine can be fitted through a statetransition matrix value of limited dimensions according to relatedtheories of a Koopman operator, that is, a search matrix A_(lift)enables ∥Y_(lift)−A_(lift)X_(lift)∥₂ to be minimum; and an optimizationproblem is solved and a wind turbine dynamic model is obtained throughan algebra operation as follows:

A _(lift) =Y _(lift) X _(lift) ^(†)  (7)

Wherein, † denotes a pseudo-inverse operation of a matrix. From acontrol perspective, it is also necessary to split a matrix A_(lift)according to dimensional number of a high-dimension observation spaceand dimensional number of an input quantity; for a high-dimensionmapping function structure employed by the method, a sub-block on a leftupper side 4×4 of a matrix A_(lift) is split as a state transitionmatrix A of a dynamic equation, and a sub-block on a right upper side4×2 of a matrix A_(lift) is split to obtain an input matrix B. By now, awind turbine high-dimension linear dynamic model via dynamic modedecomposition can be represented as the following form:

ψ(θ_(k+1) ,u _(k+1))=Aψ(ω_(k) ,u _(k))+Bu _(k)  (8)

S3: A Central Wind Site Control Model

According to a dynamic mode decomposition method, a dynamic model of Mpower generation units in a wind site can be obtained.

ψ(ω_(k+1) ^(i) ,u _(k+1) ^(i))=A _(i)ψ(ω_(k) ^(i) ,u _(k) ^(i))+B _(i) u_(k) ^(i)=1,2, . . . ,M  (9)

on such a basis, a state vector in a central control model is defined asfollows:

$\begin{matrix}{\chi_{k} = \begin{bmatrix}{\psi\left( {\omega_{k}^{1},u_{k}^{1}} \right)} \\\vdots \\{\psi\left( {\omega_{k}^{M},u_{k}^{M}} \right)}\end{bmatrix}_{4M \times 1}} & (10)\end{matrix}$

meanwhile, an input vector in a central control model is defined asfollows:

$\begin{matrix}{\eta_{k} = \begin{bmatrix}u_{k}^{1} \\\vdots \\u_{k}^{M}\end{bmatrix}_{2M \times 1}} & (11)\end{matrix}$

A control model corresponding to a central state vector is provided fromformula (9):

χ_(k+1) =Aχ _(k) +Bη _(k)  (12)

Wherein, a matrix A,B can be structured according to the followingdiagonal forms by a state transition matrix of each power generationunit:

$\begin{matrix}{A = \begin{bmatrix}A_{1} & \; & \; \\\; & \ddots & \; \\\; & \; & A_{M}\end{bmatrix}} & (13) \\{B = \begin{bmatrix}B_{1} & \; & \; \\\; & \ddots & \; \\\; & \; & B_{M}\end{bmatrix}} & (14)\end{matrix}$

Wherein, A₁ . . . A_(M) respectively denotes a state transition matrixof M power generation units, and B₁ . . . B_(M) respectively denotes aninput matrix of M power generation units.

It can be seen that the matrix A,B structured in this manner is providedwith a special sparsity structure, so as to provide more convenientconditions for fast solution of an on-line dynamic optimization controlproblem.

S4: On-Line Dynamic Optimization

On the basis of obtaining a wind turbine linear dynamic model through adata-driven method, a wind farm dynamic optimization control algorithmcan be represented as indicated by formula (15) according to a generalform of a model prediction and control framework:

$\begin{matrix}{{\min\limits_{u_{k},\chi_{k}}{J\left( {\left( \upsilon_{k} \right)_{k = 0}^{T - 1},\left( \chi_{k} \right)_{k = 0}^{T}} \right)}}{{{{subject}\mspace{14mu}{to}\mspace{14mu}\chi_{k + 1}} = {{A\chi_{k}} + {B\;\upsilon_{k}}}},{k = 0},\ldots\mspace{14mu},{T - 1}}{{{{E_{k}\chi_{k}} + {F_{k}\upsilon_{k}}} \leqslant b_{i}},{k = 0},\ldots\mspace{14mu},{T - 1}}{{E_{T}\chi_{T}} \leqslant b_{T}}} & (15)\end{matrix}$

Wherein, is a prediction range length of a model prediction and controlalgorithm and a target function is shown in the following form:

$\begin{matrix}{{J\left( {\left( \upsilon_{k} \right)_{k = 0}^{T - 1},\left( \chi_{k} \right)_{k = 0}^{T}} \right)} = {{\chi_{T}^{\top}Q_{T}\chi_{T}} + {q_{T}^{\top}\chi_{T}} + {\sum\limits_{k = 0}^{T - 1}{\chi_{k}^{\top}Q_{k}\chi_{k}}} + {\upsilon_{k}^{\top}R_{k}\upsilon_{k}} + {q_{k}^{\top}\chi_{k}} + {r_{k}^{\top}\upsilon_{k}}}} & (16)\end{matrix}$

Wherein, Q_(k), Q_(T) is a positive semi-definite target coefficientmatrix of a state variable at time k and time T, R_(k) is a positivesemi-definite target coefficient matrix of an input variable at timeq_(k) ^(T), q_(T) ^(τ) is a target coefficient vector of a statevariable at time k and time T, r_(k) ^(τ) is a target coefficient vectorof an input variable at time k, E_(k) is a state variable boundaryconstraint coefficient matrix at time k, F_(k) is an input variableboundary constraint coefficient matrix at time k, and b_(k) is aboundary constraint coefficient vector at time k. Design of acoefficient matrix and a coefficient vector depends on a wind sitedynamic optimization control objective. Q_(k), R_(k) is a positivesemi-definite coefficient matrix, a matrix E_(k), F_(k) and a vectorb_(k) correspond to a state quantity at time k and a boundary constraintof an input quantity respectively, E_(T), b_(T) is a boundary constraintof a state quantity at time T, and χ_(T) is a state quantity at time T.Design of a coefficient matrix and a coefficient vector depends on awind site dynamic optimization control objective.

In the problem of frequency modulation for wind power, the controlobjective needs to be optimized in two aspects: wind farm activefrequency modulation instruction's following effect and transientstability of a rotation speed of a power generation unit. Therefore, byusing a fluctuation degree of a wind turbine rotation speed to measureits transient stability, the following optimization objective is given:

$\begin{matrix}{\min\limits_{P_{ref}}{\sum\limits_{i = 1}^{M}\left( {{\sum\limits_{k = 0}^{T - 1}{{{\Delta\; P_{{ref},k}^{i}} - {K_{df}\Delta\; f}}}_{2}} + {Q_{x}{\sum\limits_{k = 0}^{T - 1}{{\omega_{k + 1}^{i} - \omega_{k}^{i}}}_{2}}}} \right)}} & (17)\end{matrix}$

Wherein, an active adjusting amount ΔP_(ref,k) ^(i) is defined as:

ΔP _(ref,k) ^(i) =P _(ref,k) ^(i) −P _(MPPT,k) ^(i)  (18)

formula (18) denotes an adjusting amount of a wind turbine activeinstruction P_(ref,k) ^(i) relative to a control instruction P_(MPPT,k)^(i) provided by a local controller under a maximum power trackingmodel.

ΔP _(ref,k) ^(i) =P _(ref,k) ^(i) −P _(deload,k) ^(i) =P _(ref,k) ^(i)−R _(d) ·P _(MPPT,k) ^(i)  (19)

wherein, P_(deload,k) ^(i) is an active instruction of a load-reductionwork mode and R_(d) is a load-reduction amplitude coefficient; afrequency offset amount is defined as:

Δf=f _(meas) −f _(ref)  (20)

formula (20) denotes an offset amount of a grid entry point measurementfrequency f_(meas) relative to a reference frequency f_(ref). Aparameter K_(df) is a droop coefficient of a wind farm in an externalpower-frequency feature curve and Q is a weighting coefficient forbalancing two optimization objectives. By adjusting an activeinstruction based on a local control instruction, a first item

$\sum\limits_{i = 1}^{M}{\sum\limits_{k = 0}^{T - 1}{{{\Delta P_{{ref},k}^{i}} - {K_{df}\Delta\; f}}}_{2}}$

of an optimization objective in formula (17) enables allocation of awind turbine frequency modulation task to be performed on the basis ofconsidering a respective power generation level so as to enable anoverall allocation of an active output to correspond to a wind turbinelocal working condition, such that a wind farm group also ensuresoverall wind energy transformation effects of the wind farm group whileproviding a frequency modulation service. By optimizing a fluctuationdegree of a wind turbine rotation speed, a second item

$Q_{x}{\sum\limits_{i = 1}^{M}{\sum\limits_{k = 0}^{\tau - 1}{{\omega_{k + 1}^{i} - \omega_{k}^{i}}}_{2}}}$

of an optimization objective enables a wind turbine operation state morestable, so as to reduce mechanical fatigue of a wind turbine which iscaused by participation of the wind turbine in a frequency modulationresponse process, and is added to a gearbox and other fragile mechanicalcomponents, thereby prolonging the service life of the wind turbine.

On the basis of the optimization objective, a timing sequenceconstraint, a state boundary constraint, an input boundary constraintand an initial state constraint of a central state vector are providedand respectively indicated as formula (21), formula (22), formula (23)and formula (24):

χ_(k+1) =Aχ _(k) +Bv _(k) ,k=0,1, . . . ,T−1  (21)

ω_(min)

ω_(k) ^(i)=ψ(ω_(k) ^(i) ,u _(k) ^(i))(1)

ω_(max) ,i=1, . . . ,M,k=1, . . . ,T  (22)

P _(ref,min)

u _(k) ^(i)(1)

P _(ref,max) ,k=0,1, . . . ,T−1  (23)

χ₀=[ψ(ω₀ ¹ ,u ₀ ¹) . . . ψ(ω₀ ^(M) ,u ₀ ^(M))]^(τ)  (24)

Wherein, χ₀ denotes an initial state of a central state vector χ_(k),and

formula (17) to formula (24) constitute a complete wind site frequencydynamic optimization control method. Since both a constraint conditionand a target function have concavity, thus the entire model constitutesa secondary planning problem belonging to convex optimization, which canbe rapidly and accurately solved through the current optimizationsolution procedure.

The present invention provides a data-driven control method based ondynamic mode decomposition for dynamic frequency control of a high-ratewind power independent power system. The method enables a low-dimensionnonlinear dynamic feature of a wind power system to perform globalcapturing in a high-dimension space through a state transition matrixgiven by a Koopman operator theory, thus fewer data samples arenecessary while control requirements are satisfied with respect to amodel fitting accuracy. Meanwhile, a pure linear feature of a controlmodel also provides a favorable foundation for fast on-line dynamicresponse, thereby satisfying response accuracy and speed requirementssimultaneously in an actual control step.

Although the present invention is described in detail with reference tothe foregoing embodiments, the person skilled in the art shouldunderstand that they may still make modifications to the technicalsolutions described in the foregoing embodiments or make equivalentreplacements to some technical features thereof. These modifications orreplacements do not enable the essence of the corresponding technicalsolutions to depart from the spirit and scope of the technical solutionsof the embodiments of the present invention.

What is claimed is:
 1. A data-driven wind farm frequency control methodbased on dynamic mode decomposition, wherein the method comprises thefollowing steps: S1: building a state equation of a power generationunit; S2: mapping state data in the state equation to a high-dimensionobservation state vector through an observation function, therebyobtaining a wind turbine high-dimension linear dynamic model through amatrix algebra operation; S3: according to a dynamic mode decompositionmethod in the step S2, obtaining a dynamic model of the power generationunit in a wind site; and further defining a state vector in a centralcontrol model while defining a wind speed of the power generation unitand an input vector of an active instruction, thereby obtaining acentral wind farm control model; and S4: according to a wind farm activefrequency modulation instruction and a wind turbine rotation speedfluctuation degree, designing a control optimization objective; andobtaining a constraint condition of a central state vector based on theoptimization objective, thus building a complete wind farm frequencydynamic optimization control method.
 2. The data-driven wind farmfrequency control method based on dynamic mode decomposition accordingto claim 1, wherein the state equation of the power generation unit inthe step S1 is indicated by formula (1):ω_(k+1) =f(ω_(k) ,u _(k))  (1) Wherein, ω_(k) denotes a wind turbinerotation speed at time k, f denotes a nonlinear state transitionrelation function and an input variable u_(k) is defined as:$\begin{matrix}{u_{k} = \begin{bmatrix}P_{{ref},k} \\\upsilon_{w,k}\end{bmatrix}} & (2)\end{matrix}$ Wherein, P_(ref,k) is an active instruction of an externalinput and v_(w,k) is a current wind speed; a state transition relationof the power generation unit is mainly comprised in a data pair having atiming sequence correspondence relation, which is denoted as:X=[x ₁ x ₂ . . . x _(N)],Y=[y ₁ y ₂ . . . y _(N)]  (3) wherein,$\left( {{x_{k} = \ \begin{bmatrix}\omega_{k} \\u_{k}\end{bmatrix}},{y_{k} = \ \begin{bmatrix}\omega_{k + 1} \\u_{k + 1}\end{bmatrix}}} \right)$ is a data pair at time k, with N pairs intotal.
 3. The data-driven wind farm frequency control method based ondynamic mode decomposition according to claim 1, wherein in the step S2,for state data (ω_(k), u_(k)) at time k, an observation function Ψeffects, thereby obtaining a high-dimension observation state vector:$\begin{matrix}{{\Psi\left( {\omega_{k},u_{k}} \right)} = {\begin{bmatrix}\omega_{k} \\\frac{1}{\upsilon_{\omega,k}} \\e^{{- {0.1}}\omega_{k}\upsilon_{\omega,k}} \\\omega_{k}^{2} \\u_{k}\end{bmatrix} = \begin{bmatrix}{\psi\left( {\omega_{k},u_{k}} \right)} \\u_{k}\end{bmatrix}}} & (4)\end{matrix}$ a mapping transformation effects for each column of aninitial data set, thereby obtaining a high-dimension observation setmatrix:X _(lift)=[Ψ(ω₁ ,u ₁)Ψ(ω₂ ,u ₂) . . . Ψ(ω_(N) ,u _(N))]Y _(lift)=[Ψ(ω₂ ,u ₂)Ψ(ω₃ ,u ₃) . . . Ψ(ω_(N+1) ,u _(N+1))]  (5) fortrail data of a high-dimension observation space, a search matrix Aenables ∥Y_(lift)−A_(lift)X_(lift)∥₂ to be minimum; and an optimizationproblem is solved through an algebra operation indicated by formula (6):A _(lift) =Y _(lift) X _(lift) ^(†)  (6) Wherein, † denotes apseudo-inverse operation of a matrix; from a control perspective, amatrix A_(lift) is split according to dimensional number of ahigh-dimension observation space and dimensional number of an inputquantity; for a high-dimension mapping function structure employed bythe method, a sub-block on a left upper side 4×4 of a matrix A_(lift) issplit as a state transition matrix A of a dynamic equation, and asub-block on a right upper side 4×2 of a matrix A_(lift) is split toobtain an input matrix B; and a wind turbine high-dimension lineardynamic model is obtained as indicated by formula (7):ψ(θ_(k+1) ,u _(k+1))=Aψ(ω_(k) ,u _(k))+Bu _(k)  (7)
 4. The data-drivenwind farm frequency control method based on dynamic mode decompositionaccording to claim 1, wherein in the step S3, the dynamic model of Mpower generation units in the wind site is indicated by formula (8):ψ(ω_(k+1) ^(i) ,u _(k+1) ^(i))=A _(i)ψ(ω_(k) ^(i) ,u _(k) ^(i))+B _(i) u_(k) ^(i)=1,2, . . . ,M  (8) on such a basis, a state vector in acentral control model is defined as indicated by formula (9):$\begin{matrix}{\chi_{k} = \begin{bmatrix}{\psi\left( {\omega_{k}^{1},u_{k}^{1}} \right)} \\\vdots \\{\psi\left( {\omega_{k}^{M},u_{k}^{M}} \right)}\end{bmatrix}_{4M \times 1}} & (9)\end{matrix}$ meanwhile, an input vector in a central control model isdefined as indicated by formula (10): $\begin{matrix}{\eta_{k} = \begin{bmatrix}u_{k}^{1} \\\vdots \\u_{k}^{M}\end{bmatrix}_{2M \times 1}} & (10)\end{matrix}$ a control model corresponding to a central state vector isprovided from formula (8):χ_(k+1) =Aχ _(k) +Bη _(k)  (11) Wherein, a matrix A,B is respectivelystructured according to diagonal forms of formula (12) and formula (13)by a state transition matrix of each power generation unit:$\begin{matrix}{A = \begin{bmatrix}A_{1} & \; & \; \\\; & \ddots & \; \\\; & \; & A_{M}\end{bmatrix}} & (12) \\{B = \begin{bmatrix}B_{1} & \; & \; \\\; & \ddots & \; \\\; & \; & B_{M}\end{bmatrix}} & (13)\end{matrix}$ Wherein, A₁ . . . A_(M) respectively denotes a statetransition matrix of M power generation units, and B₁ . . . B_(M)respectively denotes an input matrix of M power generation units.
 5. Thedata-driven wind farm frequency control method based on dynamic modedecomposition according to claim 1, wherein in the step S4, theoptimization objective is indicated by formula (14): $\begin{matrix}{\min\limits_{P_{ref}}{\sum\limits_{i = 1}^{M}\left( {{\sum\limits_{k = 0}^{T - 1}{{{\Delta\; P_{{ref},k}^{i}} - {K_{df}\Delta\; f}}}_{2}} + {Q_{x}{\sum\limits_{k = 0}^{T - 1}{{\omega_{k + 1}^{i} - \omega_{k}^{i}}}_{2}}}} \right)}} & (14)\end{matrix}$ wherein an active adjusting amount ΔP_(ref,k) ^(i) isdefined as:ΔP _(ref,k) ^(i) =P _(ref,k) ^(i) −P _(MPPT,k) ^(i)  (15) formula (15)denotes an adjusting amount of a wind turbine active instructionP_(ref,k) ^(i) relative to a control instruction P_(MPPT,k) ^(i)provided by a local controller under a maximum power tracking model, aparameter K_(df) is a droop coefficient of a wind farm in an externalpower-frequency feature curve, Δf is a frequency offset amount and Q_(x)is a weighting coefficient for balancing two optimization objectives; ifa current wind farm adopts a load-reduction work mode, a correspondingactive adjusting reference changes into:ΔP _(ref,k) ^(i) =P _(ref,k) ^(i) −P _(deload,k) ^(i) =P _(ref,k) ^(i)−R _(d) ·P _(MPPT,k) ^(i)  (16) Wherein, P_(deload,k) ^(i) is an activeinstruction of a load-reduction work mode and R_(d) is a load-reductionamplitude coefficient; a frequency offset amount is defined as:Δf=f _(meas) −f _(ref)  (17) formula (17) denotes an offset amount of agrid entry point measurement frequency f_(meas) relative to a referencefrequency f_(ref).
 6. The data-driven wind farm frequency control methodbased on dynamic mode decomposition according to claim 1, wherein in thestep S4, the constraint condition of the central state vector is atiming sequence constraint, a state boundary constraint, an inputconstraint and an initial state constraint, which are respectivelyindicated as formula (18), formula (19), formula (20) and formula (21):χ_(k+1) =Aχ _(k) +Bv _(k) ,k=0,1, . . . ,T−1  (18)ω_(min)

ω_(k) ^(i)=ψ(ω_(k) ^(i) ,u _(k) ^(i))(1)

ω_(max) ,i=1, . . . ,M,k=1, . . . ,T  (19)P _(ref,min)

u _(k) ^(i)(1)

P _(ref,max) ,k=0,1, . . . ,T−1  (20)χ₀=[ψ(ω₀ ¹ ,u ₀ ¹) . . . ψ(ω₀ ^(M) ,u ₀ ^(M))]^(τ)  (21) Wherein, χ₀denotes an initial state of a central state vector χ_(k), and formula(14) to formula (21) constitute a complete wind farm frequency dynamicoptimization control method.